Step-by-step explanation:
To find the values of \( A \) and \( B \) such that \( AX + BY \) equals a given vector, we are given:
\[ A = [4, 6] \]
\[ B = [1, 3] \]
Let's denote the vector \( X \) as \( X = [x_1, x_2] \) and \( Y \) as \( Y = [y_1, y_2] \). The expression \( AX + BY \) can be calculated as follows:
\[ AX + BY = [4x_1 + 1y_1, 6x_2 + 3y_2] \]
The vector resulting from \( AX + BY \) needs to match the vector we are given. According to the problem, this vector is not explicitly stated, but if we are to find \( A \) and \( B \) such that \( AX + BY = [8, 15] \), we set up the following equations:
\[ 4x_